National borders transcended: the impact of geographical proximity on the growth of global innovation networks among cities in East Asia

Figures & data

Figure 1. Number of inventors by countries in US Patents.

Table 1. Database of co-invention network.

Period	2001–2004	2005–2008	2009–2012	2013–2016
Density	1.82E-5	1.64E-5	1.31E-5	1.08E-5
Number of Nodes	153868	165179	224438	296955
Number of Links	431446	450051	661453	957011
Number of joint patents	413578	441557	669380	965199
Number of All Patents	1465264	2802875	4566695	4841129

Figure 2. Network dynamics of East Asia.

Table 2. Fitted power law distribution.

Exponent α	3.217
Cutoff (xmin)	36
Log-likelihood	−59694.8
KS test statistic	0.014
p-value*	0.004

*H0 rejected at significance level 0.05.

Figure 3. Power node distribution by country.

Table 3. Centrality of each time period.

Index	Period	Japan	Hongkong	South Korea	North Korea	China	Taiwan	Singapore
Closeness	2001–2004	990	0	1	0	0	0	0
	2005–2008	981	0	0	0	0	0	1
	2009–2012	762	0	193	0	17	0	0
	2013–2016	87	4	606	0	236	1	3
Betweeness	2001–2004	826	1	85	0	2	71	0
	2005–2008	737	1	138	0	13	95	1
	2009–2012	607	1	181	0	79	101	1
	2013–2016	485	6	211	0	170	85	4

Figure 4. Structural power nodes plot.

Figure 5. Average HHI for each period.

Figure 6. Bubble chart by group size for each period.

Table 4. List of metropolitan areas and populations.

	City (region)	Population of central city (2016)
1	Tokyo	37900000
2	Seoul	24105000
3	Shanghai	23390000
4	Beijing	20415000
5	Osaka-Kobe-Kyoto	17075000
6	Nagoya-Aichi	10070000
7	Taipei	8550000
8	Hong Kong-Shenzhen	7330000
9	Singapore	5825000
10	Daejeon	1535191

Figure 7. Heat map of GIN among major cities (regions).

Figure 8. Map of network in the metropolitan areas of East Asia.

Table 5. Overview of determinants.

Period: 2001–2004
Index	Min	Max	Mean	SD
y: Number of co-inventions over 4 years	0	7237.80	270.51	1105.27
X1: The product of inventors per million population in two metropolitan areas	0.64	12.20	7.05	2.76
X2: Inverse of the square of the Euclidean distance	3.38E−8	6.00E−5	4.04E−6	1.25E−5
Period: 2005–2008
Index	Min	Max	Mean	SD
y: Number of co-inventions over 4 years	0	14310.47	581.74	2197.26
X1: The product of inventors per million population in two metropolitan areas	2.98	12.32	8.11	2.19
X2: Inverse of the square of the Euclidean distance	3.38E−8	6.00E−5	4.04E−6	1.25E−5
Period: 2009–2012
Index	Min	Max	Mean	SD
y: Number of co-inventions over 4 years	0	8820.49	459.37	1514.51
X1: The product of inventors per million population in two metropolitan areas	4.99	12.57	8.97	1.87
X2: Inverse of the square of the Euclidean distance	3.38E−8	6.00E−5	4.04E−6	1.25E−5
Period: 2013–2016
Index	Min	Max	Mean	SD
y: Number of co-inventions over 4 years	0.14	11728.78	668.94	2142.97
X1: The product of inventors per million population in two metropolitan areas	6.00	12.95	9.64	1.64
X2: Inverse of the square of the Euclidean distance	3.38E−8	6.00E−5	4.04E−6	1.25E−5

Table 6. Results of Negative binomial regression.

Period	2001–2004	2005–2008	2009–2012	2013–2016
Dependent variable	co-inventions	co-inventions	co-inventions	co-inventions
X1: The product of inventors per million population in two metropolitan areas	3.86E−1**	3.18 E−1*	1.91E−1	9.13E−2**
X2: Inverse of the square of the Euclidean distance	3.12E3	9.18E3	2.15E4	2.84E4*
National Dummies	−8.60E−1*	−8.87E−1*	−7.70E−1*	−7.03E−1*
Number of Observations	110	110	110	110
AICc	49.59	45.79	49.21	50.24

*p<0.05, **p<0.01.

Table 7. Results of QAP.

Period	2001–2004	2005–2008	2009–2012	2013–2016
QAP Correlations	−0.276	−0.281	−0.311	−0.318
QAP P-Values	0.002	0.002	<0.0001	<0.0001

Note: QAP = quadratic assignment procedure.